Statistics Papers

Document Type

Journal Article

Date of this Version

3-2012

Publication Source

Combinatorica

Volume

32

Issue

2

Start Page

221

Last Page

250

DOI

10.1007/s00493-012-2704-1

Abstract

We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10−42 n −3 q −30, where is the minimal statistical distance between f and the family of dictator functions.

Our results extend those of [11], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [4,6,9,15,7]) cannot hide manipulations completely.

Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s00493-012-2704-1.

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Date Posted: 27 November 2017